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How to Prove It: A Structured Approach

af Daniel J. Velleman

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521447,814 (4.14)2
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.… (mere)
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A great book on mathematical proofs for someone with very limited prior knowledge.

The exercises are great, though they are plenty and can take a considerable amount of time to work through. ( )
  kladimos | Sep 23, 2021 |
This book demonstrates proofs and shows the underlying logical machinery behind them. It focuses especially on the language of mathematical logic. This is a good thing since most of the symbols might as well be from an alien language. It is split into seven chapters with two appendices, a section on suggested further reading, a summary of proof techniques mentioned, and an index. The book also mentions Proof Building Software, but I did not check to see if the link still worked or not. ( )
  Floyd3345 | Jun 15, 2019 |
Not yet read--deals with logical and mathematical proofs using examples from a variety of fields.
  timoDM | Feb 20, 2008 |
This should be required reading for all math majors and those who want to learn how to write formal proofs. It is well written with lots of examples. ( )
  billlund | Sep 12, 2007 |
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Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

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